Certain New Subclasses of $t$-fold Symmetric Bi-univalent Function Using $Q$-derivative Operator

Abstract

In this current study, we introduced and investigated two new subclasses of the bi-univalent functions associated with $q$-derivative operator; both $f(z)$ and $f^{-1}(z)$ are $t$-fold symmetric holomorphic functions in the open unit disk. Among other results, upper bounds for the coefficients $|\rho_{t+1}|$ and $|\rho_{2t+1}|$ are found in this study. Also certain special cases are indicated.